Multiple instance learning (MIL)-based methods have been widely adopted to process the whole slide image (WSI) in the field of computational pathology. Due to the sparse slide-level supervision, these methods usually lack good localization on the tumor regions, leading to poor interpretability. Moreover, they lack robust uncertainty estimation of prediction results, leading to poor reliability. To solve the above two limitations, we propose an explainable and evidential multiple instance learning (E-MIL) framework for whole slide image classification. E-MIL is mainly composed of three modules: a detail-aware attention distillation module (DAM), a structure-aware attention refined module (SRM), and an uncertainty-aware instance classifier (UIC). Specifically, DAM helps the global network locate more detail-aware positive instances by utilizing the complementary sub-bags to learn detailed attention knowledge from the local network. In addition, a masked self-guidance loss is also introduced to help bridge the gap between the slide-level labels and instance-level classification tasks. SRM generates a structure-aware attention map that locates the entire tumor region structure by effectively modeling the spatial relations between clustering instances. Moreover, UIC provides accurate instance-level classification results and robust predictive uncertainty estimation to improve the model reliability based on subjective logic theory. Extensive experiments on three large multi-center subtyping datasets demonstrate both slide-level and instance-level performance superiority of E-MIL.